Dephasing Process of a Single Atom Interacting with a Two-Mode Field

We consider the interaction of a qubit system with a two-mode field in the presence of multi-photon transition and phase damping effect. We use the master equation to obtain the density operator when the qubit is initially prepared in its excited state and the field is in a finite-dimensional pair coherent state. The properties of the considered system, such as the population inversion, amount of the mixedness, parameter estimation, and squeezing, are explored for one- and two-photon transitions. The effects of photon addition to the field and phase damping on the evaluation of these quantumness measures are also investigated.     

Quantum jumps in Landau-Zener transitions in the dissipative dynamics of a superconducting qubit

The effect of noise on the populations of the levels of a qubit in individual experimental implementations has been studied by the quantum trajectory method. A transition to the average dynamics obtained by means of multiple measurements of the state of the qubit is analyzed. The developed method is applied to investigate the effect of noise on the interference pattern appearing in the amplitude spectroscopy of the qubit in a strong variable field owing to Landau-Zener transitions. The effect of the number of repeated measurements and the fluctuation of the phase of a pump pulse on the formation of the response of the qubit to the external field has been analyzed. This makes it possible to interpret recent experiments in terms of individual implementations and averaged dynamics.     

Optical selection rules and phase-dependent adiabatic state control in a superconducting quantum circuit

We analyze the optical selection rules of the microwave-assisted transitions in a flux qubit superconducting quantum circuit (SQC). We show that the parities of the states relevant to the superconducting phase in the SQC are well defined when the external magnetic flux phi(e) = phi(0)/2; then the selection rules are the same as the ones for the electric-dipole transitions in usual atoms. When phi(e) does not = phi(0)/2, the symmetry of the potential of the artificial "atom" is broken, a so-called delta-type "cyclic" three-level atom is formed, where one- and two-photon processes can coexist. We study how the population of these three states can be selectively transferred by adiabatically controlling the electromagnetic field pulses. Different from lambda-type atoms, the adiabatic population transfer in our three-level delta atom can be controlled not only by the amplitudes but also by the phases of the pluses.     

Coherent quasiclassical dynamics of a persistent current qubit

A new regime of coherent quantum dynamics of a qubit is realized at low driving frequencies in the strong driving limit. Coherent transitions between qubit states occur via the Landau-Zener process when the system is swept through an energy-level avoided crossing. The quantum interference mediated by repeated transitions gives rise to an oscillatory dependence of the qubit population on the driving-field amplitude and flux detuning. These interference fringes, which at high frequencies consist of individual multiphoton resonances, persist even for driving frequencies smaller than the decoherence rate, where individual resonances are no longer distinguishable. A theoretical model that incorporates dephasing agrees well with the observations.     

Dynamics of interacting qubits in a strong alternating electromagnetic field

The populations of energy levels of interacting qubits have been studied as functions of the field amplitude and other control parameters for a constant frequency of the external electromagnetic field. It has been found that the qubit coupling constant strongly affects the quantum-coherent Landau-Zener transitions between the qubit states and the formation of an interference pattern in level populations, depending on the field parameters. It has been demonstrated that it is possible to determine the qubit coupling constant by Landau-Zener interferometry.     

Two-dimensional mesoscopic vortex clusters in a superconducting ring: Shell structure and melting

The structure and phase transitions in the mesoscopic system of vortices in a quasi-two-dimensional superconducting ring are investigated. The shell structure of the mesoscopic system of vortices is studied, and its variation with the number of vortices and the parameters of the superconducting ring is analyzed. Two mechanisms of formation of new shells in vortex clusters with an increasing number of vortices in an increasing magnetic field are discovered: the generation of a new shell in a cluster and the splitting of the internal shell into two shells. The melting of vortex clusters and their thermodynamic parameters are analyzed using the Monte Carlo method. It is found that the melting of shell-type clusters occurs in two stages, orientation melting taking place at the lower temperature (during which nearly crystalline adjacent shells start rotating relative to each other) and blurring of the vortex structure occurring at the higher temperature. The shells obtained by splitting upon an increase in the number of vortices do not participate in orientational melting. The two-stage form of melting is associated with the smaller height of potential barriers being surmounted during the rotation of shells relative to one another as compared to the barrier for vortices jumping from one shell to another.     

Holographic quantum computing

We propose to use a single mesoscopic ensemble of trapped polar molecules for quantum computing. A "holographic quantum register" with hundreds of qubits is encoded in collective excitations with definite spatial phase variations. Each phase pattern is uniquely addressed by optical Raman processes with classical optical fields, while one- and two-qubit gates and qubit readout are accomplished by transferring the qubit states to a stripline microwave cavity field and a Cooper pair box where controllable two-level unitary dynamics and detection is governed by classical microwave fields.     

Parametric control of a superconducting flux qubit

Parametric control of a superconducting flux qubit has been achieved by using two-frequency microwave pulses. We have observed Rabi oscillations stemming from parametric transitions between the qubit states when the sum of the two microwave frequencies or the difference between them matches the qubit Larmor frequency. We have also observed multiphoton Rabi oscillations corresponding to one- to four-photon resonances by applying single-frequency microwave pulses. The parametric control demonstrated in this work widens the frequency range of microwaves for controlling the qubit and offers a high quality testing ground for exploring nonlinear quantum phenomena of macroscopically distinct states.     

Energy relaxation time between macroscopic quantum levels in a superconducting persistent-current qubit

We measured the intrawell energy relaxation time tau(d) approximately 24 micros between macroscopic quantum levels in the double well potential of a Nb persistent-current qubit. Interwell population transitions were generated by irradiating the qubit with microwaves. Zero population in the initial well was then observed due to a multilevel decay process in which the initial population relaxed to lower energy levels during the driven transitions. The decoherence time, estimated from tau(d) within the spin-boson model, is about 20 micros for this configuration with a Nb superconducting qubit.     

Selective measurements of superconducting qubit states by a nonlinear Josephson oscillator

Selective measurements of the states are studied for a single quantum system, viz, a Josephson qubit, by a nonlinear oscillator operating in the mesoscopic regime in which the number of quanta during measurements is varied from a few dozen to several hundreds. The quantum Monte Carlo method is used to simulate the dissipative dynamics of the qubit–oscillator system and the process of measurements of the qubit states from the change in the number of oscillator quanta. It is shown that for π-pulses in the recording of qubit states, discrimination of states is possible in single realizations (measurements), while statistical projective measurements can be made for the prepared superposition state.     

Observation of a collective mode of an array of transmon qubits

Arrays of transmon qubits coupled to a λ/2 superconducting coplanar waveguide resonator have been studied by microwave spectroscopy. The emergence of a collective mode has been discovered for a cluster of N > 5 qubits, whose coupling constant to the electromagnetic field in the resonator is √N times greater compared to a single qubit. In addition, the emergence of collective multiphoton transitions exciting higher levels of a qubit cluster has been demonstrated and the interaction of an individual qubit with such a cluster has been investigated.     

Qubit assisted probing of coherence between mesoscopic states of an apparatus

I present a general scheme through which the evidence of a superposition involving distinct states of a mesoscopic system can be probed. The scheme relies on a single qubit being coupled to a mesoscopic harmonic oscillator in such a way that it can be used to both prepare and probe a superposition of states of the oscillator. Two potentially realizable implementations, one with a single flux qubit coupled to an LC circuit, and the other with a single ion-trap qubit coupled to the collective motion of several ions, are proposed.     

Purity and Correlation of a Cavity Field Interacting with a SC Charge Qubit with a Lossy Cavity

A single-mode microwave cavity field, coupled to its reservoir, interacting generally with a superconducting charge qubit is considered. Using a certain canonical transformation for the qubit states, the system is transformed into the usual Jaynes-Cummings model. The solution of the master equation of this system, in the case of a high-Q cavity is obtained. The temporal evolution of the population inversion is explored. The effects of cavity damping on the purity of the qubit, the field and the global system state are studied. It is found that due to the coupling between the system and environment, the purity is lost. The entanglement is compared with total correlation. It is found that, with the damping parameter, the asymptotic value of the correlation measure is not null, since the global system evolves to a classically correlated state. The negativity is used as an indicator of the degree of entanglement between the qubit and the field. The results indicate the sensitivity of these aspects to change of the damping parameter.     

Fast qubit initialization in a superconducting circuit

We demonstrate an active reset protocol in a superconducting quantum circuit. The thermal population on the excited state of a transmon qubit is reduced through driving the transitions between the qubit and an ancillary qubit. Furthermore,we investigate the efficiency of this approach at different temperatures. The result shows that population in the first excited state can be dropped from 7% to 2.55% in 27 ns at 30 m K. The efficiency improves as the temperature increases. Compared to other schemes, our proposal alleviates the requirements for measurement procedure and equipment. With the increase of qubit integration, the fast reset technique holds the promise of improving the fidelity of quantum control.     

Multiplication of qubits in a doubly resonant bichromatic field

Multiplication of spin qubits arises at double resonance in a bichromatic field when the frequency of the radio-frequency (rf) field is close to that of the Rabi oscillation in the microwave field, provided its frequency equals the Larmor frequency of the initial qubit. We show that the operational multiphoton transitions of dressed qubits can be selected by the choice of both the rotating frame and the rf phase. In order to enhance the precision of dressed qubit operations in the strong-field regime, the counter-rotating component of the rf field is taken into account.     

One-directional gain and frequency selection of electromagnetic waves in a medium with a running grating of inverse population

The effects of one-directional amplification, frequency selection and transformation of time structure of electromagnetic waves (the generation of ultra-short pulses) are considered theoretically for a medium, where the creation of a running wave of atomic states inverse population is possible under excitation by coherent light beams with different frequencies and directions. These effects are due to the possibility of synchronism of a group velocity of an amplified electromagnetic wave with the phase velocity of a wave of inverse population. The general theory is applied for describing two specific cases which are observed in CdS crystals where the gain effects are caused by: 1) radiative transitions on lines generating the P-band of recombination radiation (the visible range) and 2) radiative transitions between different exciton subbands (the far IR range).     

Macroscopic resonant tunneling in an rf-SQUID flux qubit under a single-cycle sinusoidal driving

We experimentally demonstrate the observation of macroscopic resonant tunneling(MRT) phenomenon of the macroscopic distinct flux states in a radio frequency superconducting quantum interference device(rf-SQUID) under a singlecycle sinusoidal driving.The population of the qubit exhibits interference patterns corresponding to resonant tunneling peaks between states in the adjacent potential wells.The dynamics of the qubit depends significantly on the amplitude,frequency,and initial phase of the driving signal.We do the numerical simulations considering the intra-well and interwell relaxation mechanism,which agree well with the experimental results.This approach provides an effective way to manipulate the qubit population by adjusting the parameters of the external driving field.     

Parameter-tunable doublet–quadruplet transition in a three-electron quantum dot

A three-electron quantum dot under an external magnetic field was studied. A number of phase diagrams have been obtained to demonstrate how the variation of the magnetic field and/or the parameters of confinement would lead to the occurrence of doublet–quadruplet transitions. Both the confinement with parabolic potential and the square well potential have been considered. We show that the parameters of confinement alter the ground state of the quantum dot from a spin doublet to a spin quadruplet. This result indicates that the quantum dot can be used as a good candidate for qubit of a quantum computer.     

One‐Step Implementation of N‐Qubit Nonadiabatic Holonomic Quantum Gates with Superconducting Qubits via Inverse Hamiltonian Engineering

A protocol is proposed to realize one‐step implementation of the N‐qubit nonadiabatic holonomic quantum gates with superconducting qubits. The inverse Hamiltonian engineering is applied in designing microwave pulses to drive superconducting qubits. By combining curve fitting, the wave shapes of the designed pulses can be described by simple functions, which are not hard to realize in experiments. To demonstrate the effectiveness of the protocol, a three‐qubit holonomic controlled π‐phase gate is taken as an example in numerical simulations. The results show that the protocol holds robustness against noise and decoherence. Therefore, the protocol may provide an alternative approach for implementing N‐qubit nonadiabatic holonomic quantum gates.